scholarly journals Baby universes and worldline field theories

2021 ◽  
Author(s):  
Eduardo Casali ◽  
Donald M Marolf ◽  
Henry Maxfield ◽  
Mukund Rangamani
Keyword(s):  
Quantum Gravity ◽  
Path Integrals ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field ◽  
Asymptotic Boundary ◽  
One Dimensional ◽  
Abelian Algebra ◽  
Baby Universes ◽  
Made In

Abstract The quantum gravity path integral involves a sum over topologies that invites comparisons to worldsheet string theory and to Feynman diagrams of quantum field theory. However, the latter are naturally associated with the non-abelian algebra of quantum fields, while the former has been argued to define an abelian algebra of superselected observables associated with partition-function-like quantities at an asymptotic boundary. We resolve this apparent tension by pointing out a variety of discrete choices that must be made in constructing a Hilbert space from such path integrals, and arguing that the natural choices for quantum gravity differ from those used to construct QFTs. We focus on one-dimensional models of quantum gravity in order to make direct comparisons with worldline QFT.

scholarly journals ON A NEW METHOD FOR COMPUTING TRACE ANOMALIES

1994 ◽  
Vol 03 (01) ◽  
pp. 145-148 ◽  
Author(s):  
FIORENZO BASTIANELLI
Keyword(s):  
Heat Kernel ◽  
Path Integrals ◽  
New Method ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Particle Theory ◽  
Curved Spaces ◽  
Main Ideas

I describe a new method for computing trace anomalies in quantum field theories which makes use of path-integrals for particles moving in curved spaces. After presenting the main ideas of the method, I discuss how it is connected to the first quantized approach of particle theory and to heat kernel techniques.

scholarly journals RENORMALIZATION WITHOUT INFINITIES

2005 ◽  
Vol 20 (06) ◽  
pp. 1336-1345 ◽  
Author(s):  
GERARD 'T HOOFT
Keyword(s):  
Renormalization Group ◽  
Conceptual Understanding ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Renormalization Group Equations

Most renormalizable quantum field theories can be rephrased in terms of Feynman diagrams that only contain dressed irreducible 2-, 3-, and 4-point vertices. These irreducible vertices in turn can be solved from equations that also only contain dressed irreducible vertices. The diagrams and equations that one ends up with do not contain any ultraviolet divergences. The original bare Lagrangian of the theory only enters in terms of freely adjustable integration constants. It is explained how the procedure proposed here is related to the renormalization group equations. The procedure requires the identification of unambiguous "paths" in a Feynman diagrams, and it is shown how to define such paths in most of the quantum field theories that are in use today. We do not claim to have a more convenient calculational scheme here, but rather a scheme that allows for a better conceptual understanding of ultraviolet infinities.

THE PRINCIPLE OF MINIMAL SENSITIVITY APPLIED TO A NEW PERTURBATIVE SCHEME IN QUANTUM FIELD THEORY

1989 ◽  
Vol 04 (07) ◽  
pp. 1735-1746 ◽  
Author(s):  
H. F. JONES ◽  
M. MONOYIOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Dimensional Space ◽  
Exact Result ◽  
Field Theories ◽  
Quantum Field ◽  
One Dimensional ◽  
Perturbative Method ◽  
Improved Accuracy

A recently proposed perturbative method for solving a self-interacting scalar φ4 field theory consists of writing the interaction as gφ2(1+δ) and expanding in powers of δ. The method contains an ambiguity in so far as one could modify the interaction Lagrangian by a factor λ(1−δ). The truncated expansion depends on the unphysical parameter, whereas the exact result does not. We exploit this ambiguity by assigning to λ the value for which the truncated result is stationary, thus minimizing its sensitivity to λ. The technique is applied to field theories in zero-and one-dimensional space-times and gives improved accuracy as compared to fixed λ.

Quantum Field Theory

2020 ◽  
pp. 237-288
Author(s):  
Giuseppe Mussardo
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Perturbation Theory ◽  
Canonical Quantization ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Coordinate Space ◽  
Matrix Formalism ◽  
Quantum Field ◽  
Transfer Matrix Formalism

Chapter 7 covers the main reasons for adopting the methods of quantum field theory (QFT) to study the critical phenomena. It presents both the canonical quantization and the path integral formulation of the field theories as well as the analysis of the perturbation theory. The chapter also covers transfer matrix formalism and the Euclidean aspects of QFT, the field theory of the Ising model, Feynman diagrams, correlation functions in coordinate space, the Minkowski space and the Legendre transformation and vertex functions. Everything in this chapter will be needed sooner or later, since it highlights most of the relevant aspects of quantum field theory.

scholarly journals AN APPLICATION OF NEUTRIX CALCULUS TO QUANTUM FIELD THEORY

2006 ◽  
Vol 21 (02) ◽  
pp. 297-312 ◽  
Author(s):  
Y. JACK NG ◽  
H. VAN DAM
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Effective Field Theories ◽  
Quantum Gravity ◽  
Asymptotic Series ◽  
Effective Field ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Neutrix Calculus

Neutrices are additive groups of negligible functions that do not contain any constants except 0. Their calculus was developed by van der Corput and Hadamard in connection with asymptotic series and divergent integrals. We apply neutrix calculus to quantum field theory, obtaining finite renormalizations in the loop calculations. For renormalizable quantum field theories, we recover all the usual physically observable results. One possible advantage of the neutrix framework is that effective field theories can be accommodated. Quantum gravity theories will then appear to be more manageable.

scholarly journals The landscape and the multiverse: What’s the problem?

Synthese ◽  
2021 ◽  
Author(s):  
James Read ◽  
Baptiste Le Bihan
Keyword(s):  
String Theory ◽  
Quantum Gravity ◽  
Current Source ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
The Past ◽  
Empirical Criterion ◽  
Scientific Status ◽  
Vast Range

AbstractAs a candidate theory of quantum gravity, the popularity of string theory has waxed and waned over the past four decades. One current source of scepticism is that the theory can be used to derive, depending upon the input geometrical assumptions that one makes, a vast range of different quantum field theories, giving rise to the so-called landscape problem. One apparent way to address the landscape problem is to posit the existence of a multiverse; this, however, has in turn drawn heightened attention to questions regarding the empirical testability and predictivity of string theory. We argue first that the landscape problem relies on dubious assumptions and does not motivate a multiverse hypothesis. Nevertheless, we then show that the multiverse hypothesis is scientifically legitimate and could be coupled to string theory for other empirical reasons. Looking at various cosmological approaches, we offer an empirical criterion to assess the scientific status of multiverse hypotheses.

scholarly journals Wilsonian Effective Action and Entanglement Entropy

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1221
Author(s):  
Satoshi Iso ◽  
Takato Mori ◽  
Katsuta Sakai
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Effective Action ◽  
Correlation Functions ◽  
Entanglement Entropy ◽  
Feynman Diagrams ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Non Gaussian

This is a continuation of our previous works on entanglement entropy (EE) in interacting field theories. In previous papers, we have proposed the notion of ZM gauge theory on Feynman diagrams to calculate EE in quantum field theories and shown that EE consists of two particular contributions from propagators and vertices. We have also shown that the purely non-Gaussian contributions from interaction vertices can be interpreted as renormalized correlation functions of composite operators. In this paper, we will first provide a unified matrix form of EE containing both contributions from propagators and (classical) vertices, and then extract further non-Gaussian contributions based on the framework of the Wilsonian renormalization group. It is conjectured that the EE in the infrared is given by a sum of all the vertex contributions in the Wilsonian effective action.

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